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How do you differentiate #f(x)=sqrt((x^3+x^2)^-1+x^3) # using the chain rule?

1 Answer

Jul 13, 2018

#f'(x)=(-(x^3+x^2)^(-2)(3x^2+2x)+3x^2)/sqrt((x^3+x^2)^(-1)+x^3)#

Explanation:

We Need the chain rule

#(f(g(x))'=f'(g(x))*g'(x)#

so we get

#f'(x)=1/2*((x^3+x^2)^(-1)+x^3)^(-1/2)*(-(x^3+x^2)^(-2)(3x^2+2x)+3x^2)#

this is
#((-(x^3+x^2)^(-2)(3x^2+2x)+3x^2))/sqrt((x^3+x^2)^(-1)+x^3)#

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